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Date:         Wed, 4 Apr 2007 15:18:11 -0400
Reply-To:     "Burleson,Joseph A." <burleson@up.uchc.edu>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Burleson,Joseph A." <burleson@up.uchc.edu>
Subject:      Re: Chi-squared and Chi-squared test for trend comparison
Comments: To: Richard Ristow <wrristow@mindspring.com>
In-Reply-To:  <7.0.1.0.2.20070404122907.037a3008@mindspring.com>
Content-Type: text/plain; charset="us-ascii"

Richard:

The last 6 large (n = 400 to 6,000) clinical trials I analyzed all had age perfectly normally distributed (i.e., skewness between -.20 and +.20). On the other hand, I, too, have seen age not be normal (e.g., Poisson distributions, U-shaped distributions, etc.). One cannot assume that it is one way or the other for no specific reason.

Sorry to be so nit-picky, but the Central Limit Theorem has nothing at all to do with whether a population OR a single sample is normal or non-normal. The CLT has to do with "sampling" distributions. Repeated sampling of a certain sample size n, of a population (continuous variable) distribution, whether the population distribution is normal or not, but which has a mean and an SD, will produce a set of means which is normally distributed (Pagano & Gauvreau, 2000; Hays, 1973).

The CLT is almost always born out when the n of the sample that is repeated being taken is >=40, and at least 50 repeated samples are taken. I am looking for the place where these bets are made!

I accept cash, checks, VISA or future promises.

Joe Burleson

-----Original Message----- From: Richard Ristow [mailto:wrristow@mindspring.com] Sent: Wednesday, April 04, 2007 2:01 PM To: Burleson,Joseph A.; SPSSX-L@LISTSERV.UGA.EDU Subject: Re: Chi-squared and Chi-squared test for trend comparison

Another amicus remark - I seem to be making a lot, lately -

At 10:41 AM 4/4/2007, Burleson,Joseph A. wrote:

>[...] when you have a (presumably) parametric, hopefully normally >distributed variable such as age [...]

If my principles and the gullibility of others permitted, I would get very rich betting against the distribution of ages being normally distributed, in any study.

The big reason for expecting normal distributions to be common, is the central limit theorem. Its exact hypotheses will rarely be satisfied with real data. However, if a quantity may reasonably be modeled as the sum of a number of independent random quantities of similar variance, it's reasonable to take it as approximately normal.

However ages are generated, this isn't how.


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